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An exact approach to the restricted block relocation problem based on a new integer programming formulation

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  • Tanaka, Shunji
  • Voß, Stefan

Abstract

This study addresses the block(s) relocation problem (BRP), also known as the container relocation problem. This problem considers individually retrieving blocks piled up in tiers according to a predetermined order. When the block to be retrieved next is not at the top, we have to relocate the blocks above it because we can access only the topmost blocks. The objective is to retrieve all the blocks with the smallest number of relocations. In this study, a novel exact algorithm is proposed for the restricted BRP, a class of the problem where relocatable blocks are restricted. The proposed algorithm computes lower and upper bounds iteratively by solving the corresponding integer programming problems until the optimality gap is reduced to zero. The novelty of the algorithm lies in the formulations based on complete and truncated relocation sequences of the individual blocks. We examine the effectiveness of the proposed algorithm through computational experiments for benchmark instances from the literature. In particular, we report that, for the first time, all the instances with up to 100 blocks are solved to proven optimality.

Suggested Citation

  • Tanaka, Shunji & Voß, Stefan, 2022. "An exact approach to the restricted block relocation problem based on a new integer programming formulation," European Journal of Operational Research, Elsevier, vol. 296(2), pages 485-503.
    • Handle: RePEc:eee:ejores:v:296:y:2022:i:2:p:485-503
    DOI: 10.1016/j.ejor.2021.03.062
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    References listed on IDEAS

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    1. de Melo da Silva, Marcos & Toulouse, Sophie & Wolfler Calvo, Roberto, 2018. "A new effective unified model for solving the Pre-marshalling and Block Relocation Problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 40-56.
    2. Petering, Matthew E.H. & Hussein, Mazen I., 2013. "A new mixed integer program and extended look-ahead heuristic algorithm for the block relocation problem," European Journal of Operational Research, Elsevier, vol. 231(1), pages 120-130.
    3. Yat‐wah Wan & Jiyin Liu & Pei‐Chun Tsai, 2009. "The assignment of storage locations to containers for a container stack," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 699-713, December.
    4. Galle, Virgile & Barnhart, Cynthia & Jaillet, Patrick, 2018. "A new binary formulation of the restricted Container Relocation Problem based on a binary encoding of configurations," European Journal of Operational Research, Elsevier, vol. 267(2), pages 467-477.
    5. Silva, Marcos de Melo da & Erdoğan, Güneş & Battarra, Maria & Strusevich, Vitaly, 2018. "The Block Retrieval Problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 931-950.
    6. Zhang, Canrong & Guan, Hao & Yuan, Yifei & Chen, Weiwei & Wu, Tao, 2020. "Machine learning-driven algorithms for the container relocation problem," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 102-131.
    7. Bacci, Tiziano & Mattia, Sara & Ventura, Paolo, 2020. "A branch-and-cut algorithm for the restricted Block Relocation Problem," European Journal of Operational Research, Elsevier, vol. 287(2), pages 452-459.
    8. Caserta, Marco & Schwarze, Silvia & Voß, Stefan, 2012. "A mathematical formulation and complexity considerations for the blocks relocation problem," European Journal of Operational Research, Elsevier, vol. 219(1), pages 96-104.
    9. Ting, Ching-Jung & Wu, Kun-Chih, 2017. "Optimizing container relocation operations at container yards with beam search," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 17-31.
    10. Zehendner, Elisabeth & Caserta, Marco & Feillet, Dominique & Schwarze, Silvia & Voß, Stefan, 2015. "An improved mathematical formulation for the blocks relocation problem," European Journal of Operational Research, Elsevier, vol. 245(2), pages 415-422.
    11. Jovanovic, Raka & Tuba, Milan & Voß, Stefan, 2019. "An efficient ant colony optimization algorithm for the blocks relocation problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 78-90.
    12. Bortfeldt, Andreas & Forster, Florian, 2012. "A tree search procedure for the container pre-marshalling problem," European Journal of Operational Research, Elsevier, vol. 217(3), pages 531-540.
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    Cited by:

    1. Jin, Bo & Tanaka, Shunji, 2023. "An exact algorithm for the unrestricted container relocation problem with new lower bounds and dominance rules," European Journal of Operational Research, Elsevier, vol. 304(2), pages 494-514.

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